MinT - Best Known (168−47, 168, s)-Nets in Base 3

Best Known (168−47, 168, s)-Nets in Base 3

(168−47, 168, 264)-Net over F₃ — Constructive and digital

Digital (121, 168, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 56, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(168−47, 168, 484)-Net over F₃ — Digital

Digital (121, 168, 484)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−47, 168, 13709)-Net in Base 3 — Upper bound on s

There is no (121, 168, 13710)-net in base 3, because

1 times m-reduction [i] would yield (121, 167, 13710)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47 799707 937355 030184 650181 881908 806155 587671 490414 903119 475754 381254 038946 005337 > 3¹⁶⁷ [i]